Premium
Numerical solution of the Helmholtz equation with high wavenumbers
Author(s) -
Bao Gang,
Wei G. W.,
Zhao Shan
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.883
Subject(s) - helmholtz equation , wavenumber , helmholtz free energy , computation , convolution (computer science) , mathematics , dispersion (optics) , mathematical analysis , fast fourier transform , grid , algorithm , physics , computer science , geometry , optics , thermodynamics , machine learning , artificial neural network , boundary value problem
This paper investigates the pollution effect, and explores the feasibility of a local spectral method, the discrete singular convolution (DSC) algorithm for solving the Helmholtz equation with high wavenumbers. Fourier analysis is employed to study the dispersive error of the DSC algorithm. Our analysis of dispersive errors indicates that the DSC algorithm yields a dispersion vanishing scheme. The dispersion analysis is further confirmed by the numerical results. For one‐ and higher‐dimensional Helmholtz equations, the DSC algorithm is shown to be an essentially pollution‐free scheme. Furthermore, for large‐scale computation, the grid density of the DSC algorithm can be close to the optimal two grid points per wavelength. The present study reveals that the DSC algorithm is accurate and efficient for solving the Helmholtz equation with high wavenumbers. Copyright © 2003 John Wiley & Sons, Ltd.